Wednesday, June 16, 2010

setiQuest Crab Pulsar

The baudline signal analyzer was used to analyze the setiQuest Crab Pulsar (PSR B0531+21) data file. The quadrature data has a sample rate of 8738133.333 samples/second and a base frequency of 1420.0 MHz. The 9.77 GB of data is 9 minutes and 32.5 seconds in duration (572.5 seconds).

The following command line was used to stream the Crab Pulsar data files into baudline:

A 65536 point FFT for a 266.67 Hz/bin resolution was used to create the image below.

Hydrogen is the hump in the center of the spectrum at +200 kHz. A weak tone on the right side of the Average display in the bottom of the filter roll-off will be investigated in more detail below. This small tone was measured with the fundamental Hz window to be at +4315732.753 Hz. Another feature of interest are the horizontal bands in the main spectrogram display. Using the periodic bars these bands were measured to have a periodicity of 3.489 seconds.

The magnitude time domain operation was selected in the input Channel Mapping window along with a prototype summing option in the Waveform display at a timebase of 65536X to create the image below.

This looks like a sine wave that has the top of it's positive cycle clipped. Using the periodic bars again, the periodicity was measured to be 3.5 seconds. Only two and half cycles were used here which is why the above spectrogram measurement has more accuracy.

Here is the same Waveform display from a section farther into the data file.

The shape has changed from flat topped clipping to pointy peaks. A slightly more accurate periodicity was measured to be 3.458 seconds.

Hydrogen has SidebandsThe peak in the center at +200 kHz is hydrogen and it has sidebands that have a delta of ±1455 kHz. The sample rate 8738133 / 1455000 Hz = 6.0056 which is very close to the whole number six is suspicious. Sidebands with the same delta Hz were also seen in the Exoplanet 060 data analysis.

Auto DriftIn the sidebands image above there is a small peak just to left of Hydrogen near 0 Hz. We will examine this region by zooming in with a decimation factor of 64 for a 4.167 Hz/bin resolution. Below is the Average spectrum of the standard Fourier transform (green) and a version with Auto Drift (purple) enabled.

Only two peaks are visible with the Fourier transform. When Auto Drift is enabled, two new peaks appear and the original two peaks become even stronger (+1.5 dB). These four peaks will be investigated in more detail below.

-1201 HzDecimation by 4096 for a 0.0651 Hz/bin resolution. This drifting-random-walk signal has a -84.90 Hz / 572.5 seconds = -0.1483 Hz/sec drift rate. The auto drift algorithm was used in this spectrogram for about 1 dB more signal extraction power. Note that the horizontal zoom was set to Hz=2X so that the drifting signal would fit on the screen.

+49999 HzDecimation by 4096 for a 0.0651 Hz/bin resolution. This drifting-random-walk signal has a -85.16 Hz / 572.5 seconds = -0.1488 Hz/sec drift rate. The auto drift algorithm was used in this spectrogram for about 1 dB more signal extraction power. Note that the horizontal zoom was set to Hz=2X so that the drifting signal would fit on the screen.

This signal is an identical twin to the -1201 Hz signal. They are separated by 49999 - -1201 = 51200 Hz.

This signal is an identical twin to the +20173 Hz signal. They are separated by 71373.1 - 20173.1 = 51200.0 Hz.

+4315733 HzDecimation by 4096 for a 0.0651 Hz/bin resolution. This signal in the roll-off filter is the same frequency that was also examined in the PSR B0329+54 Side Skirting analysis section.

The fundamental Hz window measured the tone to be at +4315733.218 Hz which is within 0.033 Hz of the value measured in the PSR B0329+54 report. The signal was weaker and no sidebands were seen this time but the amplitude does seem to be pulsing.

The Waveform window with the prototype summing feature shows oscillations that were measured with the periodic bars to have a periodicity of roughly 3.5 seconds, the same as seen above.

Decimating by 131072 for a 0.00203 Hz/bin resolution. The Average display below shows that the single tone has spread out to 5 closely spaced tones and 2 sidebands with deltas of ±0.28 Hz.

This fractal-like behavior was also seen in the PSR B0329+54 analysis. Similar yet distinctly different.

The blip Fourier transform will be used next to explore how this signal is behaving as a function of time. The blip focus parameter was set to 2. The first spectrogram image is magnitude space and second is phase space.

This complex behavior was seen in the Exoplanet 060 analysis. Is this phenomena being generated by multiple closely spaced tones toggling on and off or is it the byproduct of beat frequencies?

Quadrature MagnitudeBaudline's Input Mapping time domain operation was set to quadrature magnitude to see the Fourier power envelope. The large elephants at 1/3, 2/3, and 3/3 Nyquist were last seen in the Exoplanet 060 data. This Average spectral plot was done with no decimation.

The strong tones at 1/3 and 2/3 have sidebands that are at ±25600, ±76800, and ±128000 Hz from the center carriers. Only half of the tone at 3/3 is visible but its lower sidebands match these delta progressions. Zooming in on the dB axis shows a lot of low level harmonic structure:

The majority of those harmonics are separated by 51200 Hz. Zooming in on the Hz axis and looking at the region of spectrum to the left of the 1/3 elephant:

Like as above, most of the spacing between tones is 51200 Hz. There are weak tones at 12800 and 25600 Hz. The 51200 Hz tone is fairly strong and a tone at 417333.7 Hz is even stronger. A number of weaker tones are scattered about with different spacings.

Filter ExtractionThe impulse response transform was used to compare the I and Q channels. To inverse the positive lag symmetry a Hilbert filter was applied to the I channel prior to calculating the impulse response. This effectively undoes quadrature. Note that the horizontal axis should be time lag (not Hz) and the vertical axis should be a linear scale (not dB).

A sharp notch at time zero within a low pass filter shape. This is very similar to what was seen in the Exoplanet 060 analysis but the with the filter shape inverted.

ConclusionThe Crab Pulsar (PSR B0531+21) has a published periodicity of about 33 milliseconds. I was unable to see any pulses of that periodicity using the same quadrature magnitude Waveform summing technique used in the PSR B0329+54 analysis.

This data file contained a number of interesting features:

Unusually shaped amplitude modulation with a period of 3.489 seconds.

Sample rate divided by hydrogen sidebands delta ±1455 kHz = 6.00

Found two pairs of twin signals that are separated by 51200 Hz.

The 1/3, 2/3, 3/3 elephants are back and they have 25600 Hz sidebands.

We don't know what is causing the random walks / narrowband signal wiggles. It could be channel propagation effects of the interstellar medium (ISM) or it could be artifacts / DSP distortions / clock jitter in the Allen Telescope Array (ATA). There has been some discussion about both of these possibilities in the setiQuest forums.

So far I've found approximately 40 drifting-random-walking signals. Every setiQuest data set, which is from a different astronomical source, has had at least one of these signals in it. This is way too many signals which leads me to believe that the source is internal to the ATA.

Ico, the "blip Fourier" transform is a blind phase locking algorithm that is based on the Fourier transform. It allows for the observation of phase changes and for fine timescale details at high zoom.

The blip Fourier transform will be in the next release of baudline which should be happening soon. As you might of read in the baudline groups the new Ubuntu 10.04 and Fedora 13 Linux distributions have created some serious problems. It is critical that I have some sort of solution for the next baudline release.

> As you might of read in the baudline groups > the new Ubuntu 10.04 and Fedora 13 Linux > distributions have created some serious > problems. It is critical that I have some > sort of solution for the next baudline release.

Anders, there haven't been any new setiQuest data analyses for two reasons:

1) These reports take a lot of CPU power, my computers are slow, and I don't have the funds to buy a new faster computer. A solution could be to run baudline on a big compute server over the Internet remotely via X11. Amazon made a generous donation to the setiQuest project of 45k hours/month of EC2 cloud processing time but for whatever unknown reason the SETI Institute doesn't want to share this wonderful resource that is basically sitting idle. So what am I going to do about this problem? I'm currently working on a number of baudline speed optimizations that should result in significantly improved performance.

2) My setiQuest mission is that of discovery. I have found so many signal artifacts in the setiQuest data that continuing to find more of the same doesn't make any sense. So I'm working on a couple new advanced signal detection algorithms that should allow me to search and find things no one else has done before. Pushing the DSP envelope is fun, finding the same ATA artifacts is not.